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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 115520.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115520.bf1 | 115520j4 | \([0, 0, 0, -154508, 23375472]\) | \(132304644/5\) | \(15415994286080\) | \([2]\) | \(442368\) | \(1.6166\) | |
| 115520.bf2 | 115520j2 | \([0, 0, 0, -10108, 329232]\) | \(148176/25\) | \(19269992857600\) | \([2, 2]\) | \(221184\) | \(1.2700\) | |
| 115520.bf3 | 115520j1 | \([0, 0, 0, -2888, -54872]\) | \(55296/5\) | \(240874910720\) | \([2]\) | \(110592\) | \(0.92343\) | \(\Gamma_0(N)\)-optimal |
| 115520.bf4 | 115520j3 | \([0, 0, 0, 18772, 1865648]\) | \(237276/625\) | \(-1926999285760000\) | \([2]\) | \(442368\) | \(1.6166\) |
Rank
sage: E.rank()
The elliptic curves in class 115520.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 115520.bf do not have complex multiplication.Modular form 115520.2.a.bf
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
